This paper advances an approach to relevance grounded on patterns of material inference called argumentation schemes, which can account for the reconstruction and the evaluation of relevance relations. In order to account for relevance in different types of dialogical contexts, pursuing also non-cognitive goals, and measuring the scalar strength of relevance, communicative acts are conceived as dialogue moves, whose coherence with the previous ones or the context is represented as the conclusion of steps of material inferences. Such inferences are described using argumentation schemes and are evaluated by considering (1) their defeasibility, and (2) the acceptability of the implicit premises on which they are based. The assessment of both the relevance of an utterance and the strength thereof depends on the evaluation of three interrelated factors: (1) number of inferential steps required; (2) the types of argumentation schemes involved; and (3) the implicit premises required.